Statistical process control (SPC) tools are used for the investigation and identification of unnatural variations in the manufacturing, industrial, and service processes. The control chart, the basic and the most famous tool of SPC, is used for process monitoring. Generally, control charts are constructed under normality assumption of the quality characteristic of interest, but in practice, it is quite hard to hold the normality assumption. In such situations, parametric charts tend to offer more frequent false alarms and invalid out-of-control performance. To rectify these problems, non-parametric control charts are used, as these have the same in-control run length properties for all the continuous distributions and are known as in-control robust. This study intends to develop a new non-parametric exponentially weighted moving average (NPEWMA) chart based on sign statistics under a ranked set sampling scheme that is hereafter named (NPREWMA-SN). The run-length profiles of the NPREWMA-SN chart are computed using the Monte Carlo simulation method. The proposed scheme is compared with NPEWMA-SN and classical EWMA-$\overline{X}$ charts, using different run length measures. The comparison reveals the in-control robustness and superiority of the proposed scheme over its competitors in detecting all kinds of shifts in the process location. A practical application related to the substrate manufacturing process is included to show the demonstration of the proposed chart.

Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.

The GARCH model is one of the most influential models for characterizing and predicting fluctuations in economic and financial studies. However, most traditional GARCH models commonly use daily frequency data to predict the return, correlation, and risk indicator of financial assets, without taking data with other frequencies into account. Hence, financial market information may not be sufficiently applied to the estimation of GARCH-type models. To partially solve this problem, this paper introduces intraday high-frequency data to improve estimation of the volatility function of a semiparametric GARCH model. To achieve this objective, a semiparametric volatility proxy model was proposed, which includes both symmetric and asymmetric cases. Under mild conditions, the asymptotic normality of estimators was established. Furthermore, we also discuss the impact of different volatility proxies on estimation precision. Both the simulation and empirical results showed that estimation of the volatility function could be improved by the introduction of high-frequency data.

This work is devoted to the study of the parameter test for the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. Based on the daily GARCH model, using the parameter estimator obtained by intraday high-frequency data, the adjusted Likelihood Ratio test statistic and Wald test statistic are provided. Asymptotic distributions of the two adjusted test statistics are deducted and a way to select the optimal sampling frequency is also discussed. Simulation studies show that the proposed test statistics have better size and power than traditional ones (without using intraday high-frequency data). An empirical study is given to illustrate the potential applications of the proposed tests. The results show the idea of this article is of certain superiority and it can be extended to other GARCH type models.